On rationality of vertex operator superalgebras

TL;DR

This paper investigates the conditions under which the rationality of vertex operator superalgebras and their fixed point subalgebras are equivalent, providing new insights into their module structures and automorphism groups.

Contribution

It establishes that g-rationality of a vertex operator superalgebra implies the rationality of its fixed point subalgebra and describes the module structure, extending understanding of automorphism group actions.

Findings

g-rationality of V implies rationality of V^G

Irreducible V^G-modules are submodules of g-twisted V-modules

Rationality of V^G implies g-rationality of V for solvable G

Abstract

It is proved that g-rationality of a vertex operator superalgebra V=V_{\bar0}+V_{\bar1} for all g in G imply rationality of V^G, and also imply that each irreducible V^G-module is a submodule of an irreducible g-twisted V-module for some g in G, where G is any finite abelian subgroup of Aut(V). We also prove that for any finite solvable G, rationality of V^G implies g-rationality of V for any g in G.